Methods and systems for detecting symbol erasures

ABSTRACT

A technique for determining a symbol erasure threshold for a received communication signal containing symbol information is disclosed. The technique begins by performing a first threshold calculation to produce an initial symbol erasure threshold, then performing a first margin calculation to produce an initial symbol erasure margin and then modifying the initial symbol erasure threshold using the initial symbol erasure margin to produce a modified symbol erasure threshold. By then periodically modifying the modified symbol erasure threshold adaptive via updating the symbol erasure threshold and/or symbol erasure margin based on various error quantities, the technique can compensate for time-variant considerations, such as drifting noise levels.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/422,864: Filed Nov. 1, 2002.

BACKGROUND OF THE INVENTION

1. Field of Invention

This invention relates to methods and systems for detecting erasures ina stream of symbols.

2. Description of Related Art

Generally, digital communication channels have the capacity to transporta stream of digital data at a determinable rate with the caveat that anumber of symbols within the data stream will be corrupted. One primaryreason behind this data corruption is that communication channels sufferfrom noise contamination. That is, as data is transported through agiven communication channel, any resident noise within the communicationchannel will contaminate the data stream. As a result, any devicereceiving the corrupted data will have to compensate for symbol errorsthat will arise due to this noise contamination.

In order to address this problem, a number of error correction schemeshave been devised to detect and correct corrupted symbols. For example,a number of block codes, such as the Reed-Solomon (RS) code and the moregeneral Bose-Chadhuri-Hocquenghem (BCH) code, have been developed todetect and correct multiple symbol errors within a block of data. Yet,it is to be appreciated that there is a limit on the number of symbolsthat a given correction scheme can address for a given block of codeddata, and that the performance of these detection/correction schemessuffers when used with large block lengths.

However, it is well known in the communication arts that if thepositions of symbol errors are known a priori, then the error correctioncapacity of a given RS block of data can be doubled. While the locationsof corrupted symbols within a block of data are generally unknown priorto decoding, in some cases it is nonetheless sometimes possible todetermine the locations of symbol errors prior to decoding. When symbolsare characterized by an unknown error value but a known error location,these symbols are referred to as “erasures”. When an erasure isdetected, it is advantageous to mark the erasure's location in somemanner so that a block decoding device can utilize the additionalinformation in the decoding process.

While there are a number of known techniques used to detect symbolerasures, these techniques still often fail to appropriately marksymbols that can clearly be recognized as erasures. Furthermore, suchtechniques can also mischaracterize erasures as good data. Accordingly,new techniques to detect symbol erasures are desirable.

SUMMARY OF THE INVENTION

In various embodiments, a technique for determining a symbol erasurethreshold for a received signal containing symbol information isdisclosed. The technique begins by performing a first thresholdcalculation to produce an initial symbol erasure base-threshold, thenperforming a first margin calculation to produce an initial symbolerasure margin and then modifying the initial symbol erasurebase-threshold using the initial symbol erasure margin to produce amodified symbol erasure threshold.

By modifying a symbol erasure threshold to have a margin other than 0db, the present invention avoids missing the detection of an excessivenumber of erasures resulting from burst errors that would bemischaracterized by previously known devices. Furthermore, by making themodified symbol erasure threshold adaptive by periodically updating thesymbol erasure base-threshold and/or symbol erasure margin based onvarious error quantities, the present invention further avoidsmischaracterizing symbol erasures due to time-variant noiseconsiderations. Others features and advantages will become apparent fromthe following figures and descriptions of various embodiments.

DESCRIPTION OF THE DRAWINGS

The invention is described in detail with regard to the followingfigures, wherein like numerals reference like elements, and wherein:

FIG. 1 is a block diagram of an exemplary communication system withwhich the invention may be implemented;

FIG. 2 is a functional representation of the communication channel ofFIG. 1;

FIG. 3 is a block diagram of the exemplary receiver of FIG. 1;

FIG. 4 is a block diagram of the exemplary demapper of FIG. 3;

FIG. 5 depicts an exemplary sixteen point constellation of decisionpoints for a QAM signal;

FIG. 6 depicts a distance/error value between a decision point and asymbol estimate;

FIGS. 7 a and 7 b depict two exemplary distributions of symbol estimatesabout a symbol decision point.

FIGS. 8 a and 8 b depict an exemplary difference between symbol erasurethresholds resulting from different signal-to-noise ratios; and

FIG. 9 is a flowchart outlining a exemplary operation for generatingthresholds and detecting symbol erasures according to the presentinvention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 is a block diagram of an exemplary communication system 100according to the present invention. As shown in FIG. 1, thecommunication system 100 includes a transmitter 110, a communicationchannel 120 and a receiver 130. In operation, the transmitter 110 canprovide a communication signal that contains a stream of digital symbolsto the communication channel 120. The communication channel 120 in turncan receive the transmitted communication signal and effectively conveythe energy of the communication signal to the receiver 130. Once thereceiver 130 has received the communication signal, the receiver 130 canextract the symbol information from the received signal and provide theextracted symbol information to an external device (not shown).

The exemplary communication system 100 is an Asymmetric DigitalSubscriber's Line (ADSL) type system designed according to the AmericanNational Standards Institute (ANSI) T1.413 standard and the ITU-TG.992.1 recommendation. As such, the exemplary transmitter 110 can be anADSL-type transmitter capable of transmitting a Discrete Multi-tone(DMT) signal modulated according to a Quadrature Amplitude Modulated(QAM) paradigm. Similarly, the exemplary receiver 130 can be anADSL-type receiver and the communication channel 120 can be one or moretwisted-wire pairs.

However, in various embodiments, it should be appreciated that ascommunications systems differ, the transmitter 110 can also differ to beany one of a number of different transmission sources, such as awireless RF transmitter, a transmission system employing wires, atransmitter adapted for transmitting across a coaxial cable, an opticaltransmitter, a transmitter configured to transmit across a network, suchas a telephone network or the Internet, a sonic transmitter or any otherknown or later developed device suitable for transmitting informationwithout departing from the spirit and scope of the present invention.Further, the nature of the communications system 100 may differ, thenature of the transmitted communication signal can vary accordingly toencompass any known or later developed communication paradigm withoutdeparting from the spirit and scope of the present invention.

Similarly, it should be appreciated that the receiver 130 can alsodiffer to be any one of a number of different receiving devices, such asa wireless receiver, a reception system employing wires, a receiveradapted to receive signals from a coaxial cable, a receiver adapted toreceive signals from a network, an optical receiver, a fiber opticreceiver, a sonic receiver or any other known or later developed devicesuitable for receiving information without departing from the spirit andscope of the present invention.

Further, as the forms of the transmitter 110 and receiver 130 vary, itshould be appreciated that the form of the communication channel 120 canvary accordingly. That is, in various embodiments, the transmission path130 can be a wireless link, a wired link, such as a twisted-wire pair orcoax cable, an optical link, a sonic link or any other known or laterdeveloped combination of systems, conduits and devices capable ofconveying information from a first location to a second location withoutdeparting from the spirit and scope of the present invention.

FIG. 2 is a functional model of the exemplary communication channel 120of FIG. 1. As shown in FIG. 2, the exemplary communication channel 120includes a transfer function 210 and a summing junction 220. Inoperation, a transmitted stream of digital symbols x(n) is fed to thetransfer function 210 via link 120 a. Accordingly, the transfer function210 distorts the stream of digital symbols as a function of the physicalmake-up of the communication channel 120, thus causing, for example,multi-path distortion and delay according to Eq. (1) below:y′(n)=x(n)*h(n)  (1)where the distorted signal y′(n) is the convolution of the transmittedsignal x(n) and the transfer function h(n).

The distorted signal y′(n) is then fed to the summing junction 210 wherethe distorted signal y′(n) is subjected to various noise, such asGaussian noise and impulse noise, to produce a noisy and distortedsignal y(n) according to Eq. (2) below:y(n)=y′(n)+η(n)+δ(n)  (2)where η(n) is Gaussian noise contaminating the communication channel120, and δ(n) is impulse noise contaminating the communication channel120. As the transmitted communication signal x(n) is distorted andcontaminated with noise, the resultant noisy, distorted signal y(n) canbe fed to any number of receiving devices.

FIG. 3 is a block diagram of the exemplary receiver 130 of FIG. 1. Asshown in FIG. 3, the receiver 130 contains a front-end 310, an FFTdevice 320, a frequency equalizer 330, a demapper 340 and a decoder 350.While the exemplary receiver 130 is represented as a string of discretedevices 310–350, it should be appreciated that the receiver 130 can beimplemented using any number of architectures, such as an architecturebased on a microprocessor or digital signal processor, a number of fixedelectronic circuits, a variety of programmable logic and the likewithout departing from the spirit and scope of the present invention.

In operation, the receiver 130 can receive a stream of symbols encodedand modulated according to the ADSL standard, noting that the receivedstream of symbols can be distorted and contaminated with noise. Oncereceived, the receiver 130 can provide this distorted, noisy signal tothe front-end 310. The front-end 310 in turn can receive the distorted,noisy signal and perform any number of processes on the received signal,such as filtering, electrical conditioning, amplification andanalog-to-digital conversion, as well as any other operation that mightbe useful for a particular receiver using a particular communicationstandard. Once the front-end 310 has processed the received signal, thefront-end 310 can provide the processed signal to the FFT device 320.

The FFT device 320 can receive the processed signal, and perform areal-to-complex Fast Fourier Transform on the processed signal. The FFTdevice can then feed the transformed signal to the frequency equalizer330 such that the frequency equalizer 330 can perform an equalizationprocess to compensate for the distortion caused by the transfer functionh(n) of the communication channel 120. Assuming that the frequencyequalizer 330 performs perfectly, the resultant equalized signal will befree of multi-path distortion, but will still be contaminated withGaussian and/or impulse noise. As the frequency equalizer 330 equalizesthe received signal, the frequency equalizer 330 feeds the equalizedsignal to the demapper 340.

The demapper 340 in turn can receive the equalized signal, which can bethought of as a stream of symbol estimates x′(n)≈x(n), and perform adetection process, i.e., associating symbol estimates with knowndecision points in a working constellation, while additionally markingvarious symbols as erasures when appropriate. After the stream of symbolestimates x′(n) is detected and appropriately marked, the stream ofdetected/marked symbols is provided to the decoder 350.

As the decoder 350 receives the stream of detected/marked symbols, thedecoder 350 can perform an error detection/correction process accordingto the Reed-Solomon paradigm. After the decoder 350 has processed eachblock of symbols within the stream of detected/marked symbols, thedecoder 350 can provide a stream of corrected symbols to an externaldevice (not shown) and further provide information as to the symbolerror rate (SER) back to the demapper 340.

FIG. 4 is a block diagram of the exemplary demapper 340 according to thepresent invention. As shown in FIG. 4, the exemplary demapper 340includes a processor 410, a memory 420, a detection device 430, an errorcalculator 440, a threshold calculator 450, a margin calculator 460, amarking device 470, an output device 480 and an input device 490. Thevarious components 410–490 of the demapper 340 are coupled together withan address/data bus 402. While the exemplary demapper 340 is representedin the context of a processor architecture having a number of attachedspecial-function devices 430–470, it should be appreciated that thesespecial-function devices 430–470 preferably take the form ofsoftware/firmware routines running from the memory 420. It should alsobe appreciated that the demapper 340 can otherwise be implemented usingany number of configurations or architectures, such as an architecturebased on a microprocessor or digital signal processor, a number of fixedelectronic circuits, a variety of programmable logic and the likewithout departing from the spirit and scope of the present invention.

In operation, the input device 490 under control of the processor 410can receive a communication signal containing a stream of symbolestimates, and provide the stream of symbol estimates to the memory 420as well as the detection device 430.

The detection device 430 can receive the stream of symbol estimates, andperform a detection process on each of the symbol estimates, i.e.,assign a value to each symbol estimate by associating the symbolestimate with one symbol from a constellation of known symbols. Theexemplary detection device 430 determines the value of a symbol estimatefrom the symbol decision points 522 in the constellation 510 shown inFIG. 5. That is, as the detection device 430 receives the stream ofsymbol estimates x′(n), the detection device 430 can determine whichdecision point 522 each (noisy, distorted) symbol estimate should beassociated with based on where the symbol estimate falls on theconstellation 510. That is, while an ideal (noiseless, undistorted)received symbol should always map symbol estimates exactly to one of thesixteen symbol decision points 522 of the constellation 510, practicalreceivers can only associate a symbol estimate with that symbol decisionpoint closest to the symbol estimate. For example, if a symbol estimatefalls within the top-leftmost decision area 520 of the constellation 510of FIG. 5, then the detection device 430 will determine that that symbolestimate should be associated with the top-leftmost symbol decisionpoint 522.

However, it should be appreciated that if a particular symbol estimatefails to fall within any decision area 520, but instead falls outsideboundary 530 into the tone erasure zone, then the whole tone may beconsidered an erasure. Accordingly, if the detection device 430determines that a symbol estimate falls in the tone erasure zone, thenthe detection device 430 can mark all relevant symbol estimates aserasures. After the detection device 430 has decided the value of eachsymbol estimate or determined that the whole tone is to be considered anerasure, the detection device 430 will appropriately provide a stream ofdetected signals with erasure markers (where appropriate) to the memory420 and to the error calculator 440.

The error calculator 440 can receive the stream of detected signals witherasure markers, as well as receive the stream of symbol estimates frommemory 420 and calculate any number of error profiles. Generally, an“error profile” can be any quantity based on the distance between asymbol estimate and a symbol decision point that can be used to gaugethe likelihood that the symbol estimate was accurately decided and/orwhether the symbol estimate is likely an erasure. That is, it should beappreciated that in various circumstances, a symbol estimate may beconsidered an erasure even if the symbol estimate falls within aparticular decision area 520. This is because a received signal willoccasionally suffer impulse noise that will “perturb” a symbol estimate,without necessarily displacing the symbol estimate into a tone erasurezone. Accordingly, it can be advantageous to detect and flag these typesof symbol erasures as every detected erasure can improve the errorcorrecting capacity of an RS block decoder.

To that end, the error calculator 440 can calculate any number of errorprofiles according to any known or later developed technique. Forexample, as demonstrated in FIG. 6, the error calculator 440 can simplydetermine the distance value e_(n,k) between each decision point 322 anda symbol estimate 622 for each tone k and symbol n, and add the distancevalues, then normalize the sum. Alternatively, the error calculator 440can determine an error profile based on a normalized sum of squareddistance values.

Further, it should be appreciated that in other embodiments the errorcalculator 440 can use other techniques to calculate error profiles. Forexample, the error calculator 440 can in various embodiments employ asum of weighted distances similar to that disclosed in “METHOD FORDETECTING ERASURES IN RECEIVED DIGITAL DATA” to Spuyt (U.S. Pat. No.5,636,253) herein incorporated by reference in its entirety. Stillfurther, the error calculator 440 may employ an error metric generatedfrom a specially-designed Viterbi device, or the error calculator 440may employ any number of linear, non-linear, algorithmic ornon-algorithmic approaches useful for deriving some form of errorprofile without departing from the spirit and scope of the presentinvention.

Regardless of the type of error profile used, once the error calculator440 has determined an error profile for each received symbol estimate,the error calculator 440 can provide the error profiles to the markingdevice 470.

The working of the threshold calculator 450 is described hereinbelow.First, it should be appreciated that the noise of each symbol can becomputed as the sum E of the square of normalized errors associated witheach tone as shown in Eq. (3) below:

$\begin{matrix}{E = {\sum\limits_{i \in N}\frac{{e_{i}}^{2}}{\left( 2^{- {({24 - b_{i} - {({b_{i}\;{mod}\; 2})}})}} \right)}}} & (3)\end{matrix}$where e_(i) is an error for a tone i, b_(i) is the number of bits on thetone i., and N is the total of all loaded tones used.

The goal of normalization is to normalize the variance of the noise tothe size of the decision areas on a constellation. The normalizedvariance depends on a desired tone error probability, i.e., a tone errorprobability considered acceptable, and usually in ADSL communicationsystems, the tone error probability is a function of a requested noisemargin.

As the statistical distribution of the distance/error values can beassumed Gaussian, the sum of squares E will have a χ² (chi-squared)distribution with 2N degrees of freedom. When the threshold to detect asymbol erasure is set such that a false detection of an erasure is below10⁻⁷, such a threshold can be calculated based on two parameters: theSER and the number of tones N. However, in operation, a particular SERcan be initially assumed, and the erasure detector 420 can approximatean initial symbol erasure base-threshold E₀ based on a chi-squared modelaccording to Eq. (4) below:E ₀ ≈k ₁ +N ^(0.5) k ₂ +Nk ₃  (4)where k₁, k₂ and k₃ are parameters set according to the false detectionof errored symbols and tone erasure probability. Once the initial symbolerasure base-threshold is calculated, the threshold calculator 450 canprovide the initial symbol erasure base-threshold to the margincalculator 460.

The margin calculator 460 in turn can receive the initial symbol erasurebase-threshold, determine an initial symbol erasure margin M and thencalculate a modified symbol erasure threshold E(T) according to Eq. (5)below:E(T)=Threshold BaseValue×M arg in=E ₀×10^(−M/10)  (5)

Once a connection is established, it should be appreciated that therewill likely be a lot of margin with regard to a worst case initialsymbol erasure base-threshold value. That is, the symbol erasurebase-threshold value that would provide the best results will generallybe different than the initially calculated symbol erasurebase-threshold.

One problem with previously known erasure detection techniques is thattheir threshold error rates are defined with 0 db margins. This resultsin an excessive number of burst errors that could be detected, but willnot be flagged as an erasure. Accordingly, the desired margin M can takea range of values to address this problem. For example, in variousembodiments, the margin M can be set to a fixed value, such as 6 db,which happens to coincide with the noise margin of most practicalmodems.

However, in other embodiments, the margin M can be advantageouslycalculated based on a signal-to-noise ratio (SNR) of the receivedsignal. FIGS. 7 a and 7 b show two exemplary distributions 710 a and 710b of symbol estimates about a symbol decision point. As shown in FIG. 7a, the distribution 710 a of the symbol estimates about the decisionpoint show a tight grouping due to a favorably high SNR. In contrast,the distribution 710 b of FIG. 7 b is relatively much wider than that ofdistribution 710 a due to a relatively poor SNR.

FIGS. 8 a and 8 b provide an exemplary difference between two symbolerasure thresholds 850 a and 850 b adjusted based on the distributions710 a and 710 b of FIGS. 7 a and 7 b respectively. As shown in FIGS. 8 aand 8 b, communication signals having larger SNRs may benefit fromhaving smaller overall thresholds, while signals having smaller SNRs mayrequire much greater thresholds to avoid accidental mischaracterizationof good symbols as erasures.

Returning to FIG. 4, once the margin calculator 460 has modified theinitial symbol erasure threshold, the margin calculator 460 can providethe modified symbol erasure threshold to the marking device 470.

The marking device 470, having received a modified symbol erasurethreshold and a stream of error profiles for respective determinedsymbols, can then compare each error profile against the modified symbolerasure threshold, and mark those symbols as erasures whenever therespective error profile exceeds the threshold. As the various symbolsare appropriately compared and marked, the marking device 470 can feedthe marked-up symbols to an external device via the output device 480.

While the threshold calculator 450 and margin calculator 460 togetherprovide the novel advantage described above, it should be appreciatedthat the threshold calculator 450 and margin calculator 460 can invarious embodiments additionally update their respective threshold andmargin values over time in an adaptive fashion.

For example, in a first set of embodiments, the threshold calculator 450can periodically receive various measured SER data, including falsedetection of errored symbols data and tone erasure probability data,from the decoder 350 of FIG. 3. Accordingly, the threshold calculator450 can modify the symbol erasure base-threshold based on the measuredSER.

Similarly, the margin calculator 460 can periodically determine the SNR(or other error quantity) of a received signal by, e.g., directobservation of symbol estimates, using an error profile or receiving SNRdata from another device associated with the receiver 130. The margincalculator 460 can then determine a more appropriate margin M based onthe SNR data and recalculate the modified symbol erasure threshold E(T)using Eq. (5) above. The modification of one or both of the thresholdand margin can accordingly continue as necessary. Such modifications canbe performed at predetermined intervals or for example in response todetected changes in the SER or SNR.

FIG. 9 is a flowchart outlining an exemplary operation for adaptivelycalculating a symbol erasure base-threshold and margin, and fordetecting symbol erasures according to the present invention. Theprocess starts in step 1010 where an initial SER is determined. Asdiscussed above, the initial SER can be assumed to be a particularvalue, or the SER can be derived from measured signals. The processcontinues to step 1020.

In step 1020, an initial symbol erasure base-threshold is determined asdescribed above based upon the SER of step 1010 and the number of tonesof a received signal. Next, in step 1030, a symbol erasure margin isdetermined. As discussed above, the symbol erasure margin can be set toa fixed value, or otherwise determined according to some error quantityassociated with a received communication signal, such as an SNR. Then,in step 1040, a modified symbol erasure threshold is calculated based,for example, on Eq. (5) above using the initial symbol erasurebase-threshold of step 1020 and the margin of step 1030. The processcontinues to step 1050.

In step 1050, a stream of symbol estimates is received. Next, in step1060, the symbol estimates are associated with various known, validsymbols by associating the symbol estimates with the closest symboldecision point in a relevant symbol constellation. Then, in step 1070, astream of error profiles is generated from the stream of received symbolestimates. The process continues to step 1080.

In step 1080, the various error profiles are compared with the modifiedsymbol erasure threshold of step 1040. Then, in step 1090, adetermination is made for each symbol as to whether the symbol is anerasure based on the comparison of step 1080. If a particular symbol isdetermined to be an erasure, the process jumps to step 1200; otherwise,the process continues to step 1100.

In step 1200, each symbol determined to be an erasure is appropriatelymarked, and the process continues to step 1100.

In step 1100, the marked symbol/erasure data is exported to an externaldevice, such as an RS decoder. Next, in step 1110, SER data is receivedfrom an external device, such as the RS decoder of step 1100. Theprocess continues to step 1120.

In step 1120, the symbol erasure base-threshold is updated based on anerror quantity, such as the SER data of step 1110. Next, in step 1130,the symbol erasure margin is updated based on an error quantity, such asthe SNR of the received communication signal. Then, in step 1140, themodified symbol erasure threshold is calculated based on the updatedbase-threshold and margin. The process continues to step 1150.

In step 1150, a determination is made as to whether to continue todetect symbol erasures. If erasure detection is to continue, the processjumps back to step 1150; otherwise, control continues to step 980 wherethe process stops.

It should be appreciated that the various above-described systems andmethods are preferably implemented on a digital signal processor (DSP)or other integrated circuits. However, the systems and methods can alsobe implemented using any combination of one or more general purposecomputers, special purpose computers, programmable microprocessors ormicrocontrollers and peripheral integrated circuit elements, hardwareelectronic or logic circuits, such as application specific integratedcircuits (ASICs), discrete element circuits, programmable logic devices,such as a PLD, PLA, FPGA, or PAL or the like. In general, any device onwhich exists a finite state machine capable of implementing the variouselements of FIGS. 1–4 and/or the flowcharts of FIG. 9 can be used toimplement the receiver functions.

In various embodiments where the above-described systems and/or methodsare implemented using a programmable device, such as a computer-basedsystem or programmable logic, it should be appreciated that theabove-described systems and methods can be described by any of variousknown or later developed programming languages, such as “C”, “C++”,“FORTRAN”, Pascal”, “VHDL” and the like.

Accordingly, various storage media, such as magnetic computer disks,optical disks, electronic memories and the like, can be prepared thatcan contain information that can direct a device to implement one ormore of the above-described systems and/or methods. Once anappropriately capable device has access to the information contained onthe storage media, the storage media can provide the information to thedevice, thus enabling the device to perform the above-described systemsand/or methods.

For example, if a computer disk containing the appropriate information,such as a source file, an object file, an executable file or the like,were provided to a DSP, the DSP could receive the information,appropriately configure itself and perform the functions of the variouselements of FIGS. 1–4 and/or the flowchart of FIG. 9 to implement thereceiver 130 functions. For example, the DSP could receive variousportions of information from the disk relating to different elements ofthe above-described systems and/or methods, implement the individualsystems and/or methods and coordinate the functions of the individualsystems and/or methods to determine symbol erasure thresholds and marksymbol erasures.

In still other embodiments, rather than providing a fixed storage media,such as a magnetic-disk, information describing the above-describedsystems and methods can be provided using a communication system, suchas a network or dedicated communication conduit. Accordingly, it shouldbe appreciated that various programs, executable files or otherinformation embodying the above-described systems and methods can bedownloaded to a programmable device using any known or later developedcommunication technique.

While this invention has been described in conjunction with the specificembodiments thereof, it is evident that many alternatives,modifications, and variations will be apparent to those skilled in theart. Accordingly, preferred embodiments of the invention as set forthherein are intended to be illustrative, not limiting. There are changesthat may be made without departing from the spirit and scope of theinvention.

1. A method for determining a symbol erasure threshold for a receivedsignal containing symbol information, comprising: performing a firstthreshold calculation to produce an initial symbol erasurebase-threshold; performing a first margin calculation to produce aninitial symbol erasure margin; and modifying the initial symbol erasurebase-threshold using the initial symbol erasure margin to produce amodified symbol erasure threshold.
 2. The method of claim 1, wherein theinitial symbol erasure base-threshold is calculated based on the numberof tones used by the received signal.
 3. The method of claim 2, whereinthe initial symbol erasure base-threshold is calculated based on anassumed symbol error ratio.
 4. The method of claim 1, wherein theinitial symbol erasure base-threshold is calculated based on theformula:E ₀ ≈k ₁ +N ^(0.5) k ₂ +Nk ₃ where k₁, k₂ and k₃ are parameters setaccording to a false detection of errored symbols and a tone erasureprobability, and N is the number of tones used by the received signal.5. The method of claim 1, wherein the step of modifying the initialsymbol erasure base-threshold is calculated based on the formula:E(T)=E ₀×10^(−M/10) where E(T) is the modified symbol erasure threshold,E₀ is the initial symbol erasure base-threshold and M is a desiredmargin.
 6. The method of claim 5, wherein the desired margin iscalculated based on a signal-to-noise ratio of the received signal. 7.The method of claim 5, wherein the desired margin is fixed to be 6 db.8. The method of claim 1, further comprising adaptively updating thesymbol erasure margin based on an error quantity, then recalculating themodified symbol erasure threshold based on the updated symbol erasuremargin.
 9. The method of claim 8, wherein the error quantity is asignal-to-noise ratio of the received signal.
 10. The method of claim 1,further comprising modifying the initial symbol erasure base-thresholdone or more times.
 11. The method of claim 10, wherein the step ofmodifying the initial symbol erasure base-threshold is based on at leasta measured symbol error ratio.
 12. A method for determining a symbolerasure threshold for a received signal containing symbol information,comprising: performing a first threshold calculation to produce aninitial symbol erasure base-threshold; and adaptively modifying theinitial symbol erasure base-threshold one or more times.
 13. The methodof claim 12, wherein the step of calculating the initial symbol erasurebase-threshold is based on an assumed symbol error ratio.
 14. The methodof claim 12, wherein the step of modifying the initial symbol erasurebase-threshold is based on a measured symbol error ratio.
 15. The methodof claim 14, wherein the modified symbol erasure threshold is calculatedbased on the number of tones used by the received signal.
 16. The methodof claim 12, wherein the modified symbol erasure threshold is calculatedbased on the formula:E ₀ ≈k ₁ +N ^(0.5) k ₂ +Nk ₃ where k₁, k₂ and k₃ are parameters setaccording to a false detection of errored symbols and a tone erasureprobability, and N is the number of tones used by the received signal.17. An apparatus for determining a symbol erasure threshold for areceived signal containing symbol information, comprising: a thresholdcalculator capable of calculating an initial symbol erasurebase-threshold; and a margin calculator capable of calculating a firstsymbol erasure margin, and further capable of producing a modifiedsymbol erasure threshold based on the first symbol erasure margin andthe initial symbol erasure base-threshold.
 18. The apparatus of claim17, wherein at least one of the threshold calculator and margincalculator is configured to adaptively modify their respective initialsymbol erasure base-threshold or first symbol erasure margin based on anerror condition of the received signal.